My students get creative with Desmos

Last week I introduced my students to Desmos. After doing a short lesson to show off the power and “what-if” capabilities of desmos, I pretty much let them loose on creating equation-driven art. My main objective here was for students to get a deeper understanding of linear equations, and specifically more experience with restricting the domain and/or range of a linear equation. So I showed the students how to restrict the domain and range, and my only requirement of the art is that they include at least one instance of a restricted domain/range.  Very soon the kids wanted to know how to create and manipulate parabolas, circles, sine waves, etc.  The students absolutely loved this activity; I was hearing comments like “Desmos is the best app I ever”, and “oh, now I see how that works”.  I gave them two class periods to work on their art, and told them they can complete it at home and save it to the  google folder they have shared with me. Here’s some of the artwork I received back. This first one, the Hunger Games’ Mockingjay uses 40 equations and the student worked on it for over 3 hours.

To see Mockingjay in all its glory in Desmos:  https://www.desmos.com/calculator/ihxor3kijv

To see butterfly in Desmos: https://www.desmos.com/calculator/zwmkq6gxx5

To see Birds by the Sea in Desmos: https://www.desmos.com/calculator/poq9oyptce

To see star in circles in Desmos: https://www.desmos.com/calculator/tweud3vjdw

Good Square Root Trick for your students

While in Las Vegas this past summer, I was in a magic shop, and picked up the book “Self-working Number Magic” by Karl Fulves. It has all kinds of fun number tricks to play with (on) your students. One puzzle that gave me pause was this one:

During a class discussion on square roots, Johnny wrote this equation on the board.         

It was obviously wrong, and the teacher was about to cross it out, but on second thought it looked almost right.  Is the equation correct? Almost correct? Or is it completely wrong?

Here is the answer.

Dragon Box+: a sneaky ipad game that teaches algebra

I am not sure where I heard about Dragon Box. It was from a blog, I am sure. Anyway, after getting blown away by the web version, I talked my school into purchasing the application for our student ipads (32 on a cart).

Dragon Box is sneaky because the students begin learning how to solve algebraic equations without even knowing it. The application is done so well, that very little instruction is needed. It begins solving equations using picture cards and without using hardly any words or  instructions; the students figure out very intuitively that to solve the equations (or win the “games”) they need to make the constants zero, and then the coefficient one.  Brilliant!! So now in class, when we are solving equations, I can relate to the Dragon Box ideas to help them understand the pencil/paper steps for doing the same thing. If you haven’t checked it out yet, hurry. You’ll be amazed.

Lessons Learned on 2 Step Equations

This past week I taught my 7th graders how to solve 2-step equations. But did they actually learn how? Just graded their quizzes, and the mean score was about 75%. Arghhh!

I’ve been teaching this topic for years, and this year I did a few things differently. I think a few ideas were  good, and others still need work.

The good:

• I introduced 2-step equations and how to solve them with a demonstration.  I showed the students 3 cups. I told them that the cups hold exactly the same number of paper clips. The number of paper clips in those cups along with the 6 in my hand total 18 paper clips. How many paper clips in each cup? This was awesome; in each class, the student I called on to explain their thinking on solving the problem, solved the problems exactly how we normally solve 2-step equations: “First I subtracted 6 from 18 and got 12. Then I divided by 3 since there are 3 cups. So each cup has 4 paper clips.” Sweet. I then went and explained their thinking using the variable, c, for cup and so on…  Where did I get the idea for this demonstration? In the most unlikely place: their Holt texbook. Ha, who would have thunk?
• After we concluded that a good way to solve an equation was to zero-out the constant term that is on the same side as the variable, and then to make the coefficient 1, we created a flow map (thinking map) for their notes. I think this is a great time to emphasize the vocabulary: constant, coefficeint, and term.
• I had students come to the board and work out the homework problems twice this week. Students love it, and I get to see where they are having problems.

Things needing work:

• Many students are having a difficult time with equations like 2m-3=-9.  They are not seeing the 3 as negative, so they are subtracting 3. Previous years I would have them immediately change the subtraction sign to adding the opposite. This year I was trying to get them to use inverse operations instead. Instead of subtracting 3, lets add 3.  I *thought* they were getting it, and I think they sort of did. But this is where most of the mistakes were made on the quiz. More practice with this on Monday!
• I had my students check their work, by substituting their answer into the variable. We practiced this again and again. However, I am still seeing students work where they get the answer incorrect, and then they check their work, and they rush to believe that their check is true. I somehow want them to slow down and do the check as objectively as possible…yah right.  This is  driving their teacher crazy.  Maybe some multiple choice problems would help here.